In a 5-6 quart slow cooker, with a browning option, brown chicken in oil, 8-10 minutes, and then transfer to a plate.
Add barley, broth, wine, onion, and garlic to the pot and season with salt and pepper. Then, place the chicken back in the pot on top of these ingredients.
Cover and cook on low until chicken is cooked through, approximately 2 hours.
Once fully cooked, remove the chicken and stir the peas and tarragon into the barley. Then, season with some final salt and pepper and transfer to a platter. Arrange chicken atop the barley and serve.